Answer:
34 successful free throws out of 120
Step-by-step explanation:
We can use the 28% free throw rate to predict Jai's success in shooting 120 free throws. If the 28% was calculated from throws made under similar circumstances (e.g., during an actual game), then we can predict that he'll also hit 28% of the 120 attempts:
Likely free throw successes = (28%)*(120)
(0.28)*(120) = 33.6 successful free throws out of 120. We need to round 33.6 to the nearest whole number, which makes it 34 successful free throws out of 120.
How many 3 1/4 inch pieces of yarn can be
cut from a roll that has 52 inches of yarn?
Answer:
16 peices
Step-by-step explanation:
52/3.25 = 16
When Alan Sheperd hit the golf ball on the moon, it traveled in a projectile arc and
eventually sailed to the ground. If Alan was to do the same shot on earth, how would the golf
ball's height and distance compare to the shot on the moon?
more height and less distance
more height and more distance
O less height and less distance
less height and more distance
On Earth, the golf ball would travel much farther and higher than on the moon due to the difference in gravity. On the moon, the gravity is only 1/6th the strength of Earth's, making it much easier for the golf ball to travel farther and higher. On Earth, the golf ball would travel farther and higher due to the stronger gravitational pull.
a standard deck of cards has $52$ cards divided into $4$ suits, each of which has $13$ cards. two of the suits ($\heartsuit$ and $\diamondsuit$, called `hearts' and `diamonds') are red, the other two ($\spadesuit$ and $\clubsuit$, called `spades' and `clubs') are black. the cards in the deck are placed in random order (usually by a process called `shuffling'). what is the probability that the first two cards drawn from the deck are both red?a standard deck of cards has $52$ cards divided into $4$ suits, each of which has $13$ cards. two of the suits ($\heartsuit$ and $\diamondsuit$, called `hearts' and `diamonds') are red, the other two ($\spadesuit$ and $\clubsuit$, called `spades' and `clubs') are black. the cards in the deck are placed in random order (usually by a process called `shuffling'). what is the probability that the first two cards drawn from the deck are both red?
Probability of drawing two red cards = (26/52) * (25/51) = 25/102 = 24.509%
a standard deck of cards has 52 cards divided into 4 suits, each of which has 13 cards. two of the suits (heart suit and diamond suit, called `hearts' and `diamonds') are red, the other two (spade suit and club suit, called `spades' and `clubs') are black. the cards in the deck are placed in random order (usually by a process called `shuffling'). what is the probability that the first two cards drawn from the deck are both red?
A standard deck of 52 cards has 26 red cards ( of Hearts and Diamonds) and 26 black cards ( of Spades and Clubs).
Probability of drawing the first red card = 26/52
Probability of drawing the second red card = 25/51
So, probability of drawing two red cards = (26/52) * (25/51) = 25/102 = 24.509%
To know more about probability visit brainly.com/question/30034780
#SPJ4
43. At the beginning of the month, Emika had $24 in her school cafeteria account. The table below
shows how her account balance changed over the course of three weeks. (Positive change means
money she added into her account, while negative change means money she spends.)
1.
2
Week
1
2
3
Beginning
Balance
($)
24
8
-18
Final
Balance
($)
8
-18
Change
($)
16
26
-12
Expression to show your work
24-16 = 8
8-26-18
-18--12-6
Complete the table for weeks 2-3.
How much would Emika have to deposit into the account during week 4 so that the final
balance is positive?
Answer:go to teacher 56
Step-by-step explanation:
pop op
How are 2 graphs related?
A line graph is marked by a correlation in the form of a line. The dependent variable is placed on the y-axis and the independent variable is on the x-axis.
You can see their relationship in terms of the slope. By explanation, the slope is the ratio of the change of the y-coordinates to the change of the x-coordinates (Δy/Δx). Visually, you determine the relationship of the variables by the orientation of the line as shown in the graph. If the slope is increasing, means that the two variables are increasing together.
If the slope is decreasing, it means that when x increases, y decreases. In other words, they are inversely proportional.
Read more about line graphs:
https://brainly.com/question/26233943
#SPJ4
The complete question is:
How are line graphs used to show how two variables are related?
On a coordinate plane, point b(–6, 1) is translated to b prime(–3, –2). indira uses these steps to find a rule to describe the translation. step 1 substitute the original coordinates and the translated coordinates into (x, y) right-arrow (x a, y b): b (negative 6, 1) right-arrow b prime (negative 6 a, 1 b) = b prime (negative 3, negative 2) step 2 write two equations: negative 6 a = negative 2. 1 b = negative 3. step 3 solve each equation: negative 6 a = negative 2. a = negative 2 6. a = 4. 1 b = 3. b = negative 3 minus 1. b = negative 4. step 4 write the translation rule: (x, y) right-arrow (x 4, y minus 4) which corrects indira’s first error? indira should have substituted b (negative 6, 1) right-arrow b prime (negative 3 a, negative 2 b) = b prime (negative 6, 1) in step 1. indira should have written the equations negative 6 a = negative 3 and 1 b = negative 2 in step 2. indira should have solved the equations to find that a = negative 8 and b = negative 2 in step 3. indira should have written the translation rule (x, y) right-arrow (x minus 4, y 4) in step 4.
Indira should have written the equation negative 6 + a = negative 3, and the equation 1 + b = negative 2 in step 2, as according to coordinate geometry.
For translation from point B(-6,1) to point B'(-3,-2);
Step 1 : Substitute the original coordinates and the translated coordinates into (x,y) → (x+a,y+b) ; B (negative 6,1) → B prime (negative 6 + a, 1 + b) = B prime (negative 3, negative 2)
Step 2 ( Indira's mistake) : Two equations to be written, as in coordinate geometry; first one being negative 6 + a = negative 3 ; and the second one being 1 + b = negative 2
Step 3 : Solving the equations to get the values of a and b;
a = negative 3 + 6
a = 3, and
b = negative 2 minus 1
b = -3
Step 4 : By substitution method, using values of a and b we find B prime;
original coordinates of point B = (-6,1)
Translated coordinates of point B' = (-6 + a, 1 + b)
= ((-6) + 3 , 1 + (-3))
= (-3,-2)
Thus, that is how, step-by-step using basic linear equation method, we solved for translated coordinates.
Learn more about coordinate geometry here:
https://brainly.com/question/28182497
#SPJ4
Will give brainly thanks
The domain of the function is 0≤ x ≤ 30
The range of the function is 0≤ y ≤ 75
What are domain and range of a function ?
The range of values that we are permitted to enter into our function is known as the domain of a function. In a function like f, this set represents the x values (x). The collection of values that a function can take on is known as its range. The values that the function outputs when we enter an x value are in this set.
Here, x represents the input values ( time)
from the graph,
0≤ x ≤ 30
Here, y represents the output values ( amount of water)
from the graph,
0≤ y ≤ 75
Thus, the domain of the function is 0≤ x ≤ 30
The range of the function is 0≤ y ≤ 75
To learn more about the domain and range from the given link
https://brainly.com/question/28801359
#SPJ1
Find the slope of the line passing through the points (-6, -4) and (5, -4).
slope:
Find the slope of the line passing through the points (3, 3) and (3, -6).
slope:
you can use math away app
Look at picture for question!
Allocating the congressional seats among the states in a fair manner would mean that the seats per state would be:
State A - 13 seats State B - 18 seats State C - 22 seats State D - 37 seats How to allocate the seats ?The fairest way to allocate the seats in a fair manner would be by proportional representation where the population of a state determines the seats it gets in Congress.
State A seats :
= Population / Total population x Number of seats available
= 258 / 1, 858 x 90
= 13 seats
State B seats :
= 377 / 1, 858 x 90
= 18 seats
State C seats :
= 456 / 1, 858 x 90
= 22 seats
State D seats :
= 767 / 1, 858 x 90
= 37 seats
Find out more on allocation at https://brainly.com/question/14086534
#SPJ1
a system of 5 identical components are connected in a series. if even one of the components fails, the entire system will fail. what is the probability that the system fails if the probability that each component fails is 0.1 and different components fail independently of one another.
So the probability that the system fails is 41% if the probability that each component fails is 0.1 and different components fail independently of one another.
The probability that the system fails is the probability that even one of the 5 components fails. Since the components fail independently of one another, we can use the probability of failure for each component and multiply it by the number of components to find the probability that the system fails.
The probability that the system fails is:
1 - (1 - probability of failure of one component)^(number of components)
Given that the probability of failure of each component is 0.1, the probability that the system fails would be:
1 - (1 - 0.1)^5 = 1 - 0.59 = 0.41 or 41%
So the probability that the system fails is 41% if the probability that each component fails is 0.1 and different components fail independently of one another.
To learn more about Probability
visit; brainly.com/question/30034780
#SPJ4
What are the 7 basic units?
The seven basic SI units are second, meter, kilogram, candela, ampere, mole, kelvin.
The 11th General Conference on Weights and Measures created the International System of Units, or "Système International d'Unités," in 1960. Older systems, like the Imperial system used in the UK and many other countries, were not all that simple to manage or operate, and none were globally standardized. The seven base quantities of what is now known as the International System of Quantities are defined by the International System of Units (SI) as having standard units of measurement. In particular, they comprise a fundamental set from which all other SI units can be formed.
Second (s) – Unit of Time Meter (m) – Unit of LengthKilogram (kg) – Unit of MassAmpere (A) – Unit of Electric CurrentKelvin (K) – Unit of Thermodynamic TemperatureMole (mole) – Unit of Amount of SubstanceCandela (cd) – Unit of Luminous IntensityLearn more about SI units here:
https://brainly.com/question/10865248
#SPJ4
In quadrilateral ABCD, the diagonals intersect at point T. Jasmine has used the Alternate Interior Angles Theorem to show that angle DAC is congruent to angle BCA and that angle ADB is congruent to angle CBD. Which of the following can Jasmine use to prove that triangle ATD is congruent to triangle CTB
This question is based on the concept of congruent. Therefore, the correct option is C, i.e. DA ≅ BC.
What is quadrilateral?A quadrilateral is a closed form that has four sides, four vertices, and four angles. It's made by connecting four non-collinear points. The total of quadrilateral inner angles is always 360 degrees. A quadrilateral is a closed shape with four sides. These are quadrilateral figures: Raphael was used to create this. A quadrilateral form. The form contains only one pair of parallel sides and no right angles. A quadrilateral has four straight sides and is a two-dimensional form. Examples of quadrilaterals include parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
Here,
Given:
In quadrilateral ABCD, the diagonals intersect at point T.
By the alternate interior angles theorem :
Angle DAC is congruent to angle BCA and
angle ADB is congruent to angle CBD
Definition of alternate interior angles theorem:
The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , then resulting alternate interior angles are congruent .
In given quadrilateral ABCD,
DAC ≅ BCA
ADB ≅ CBD
And to prove that ATD ≅ CTB,
Then,
DA ≅ BC
Therefore, the correct option is C, i.e. DA ≅ BC.
The idea of congruence lies at the heart of this question. As a result, the right answer is C, which is DA ≅ BC.
To know more about quadrilateral,
https://brainly.com/question/20178266
#SPJ4
This question is based on the concept of congruent. Therefore, the correct option is C, i.e. DA ≅ BC.
What is quadrilateral?A quadrilateral is a closed form that has four sides, four vertices, and four angles. It's made by connecting four non-collinear points. The total of quadrilateral inner angles is always 360 degrees. A quadrilateral is a closed shape with four sides. These are quadrilateral figures: Raphael was used to create this. A quadrilateral form. The form contains only one pair of parallel sides and no right angles. A quadrilateral has four straight sides and is a two-dimensional form. Examples of quadrilaterals include parallelograms, trapezoids, rectangles, kites, squares, and rhombuses.
Here,
Given:
In quadrilateral ABCD, the diagonals intersect at point T.
By the alternate interior angles theorem :
Angle DAC is congruent to angle BCA and
angle ADB is congruent to angle CBD
Definition of alternate interior angles theorem:
The Alternate Interior Angles Theorem states that, when two parallel lines are cut by a transversal , then resulting alternate interior angles are congruent .
In given quadrilateral ABCD,
DAC ≅ BCA
ADB ≅ CBD
And to prove that ATD ≅ CTB,
Then,
DA ≅ BC
Therefore, the correct option is C, i.e. DA ≅ BC.
The idea of congruence lies at the heart of this question. As a result, the right answer is C, which is DA ≅ BC.
To know more about quadrilateral,
https://brainly.com/question/13805601
#SPJ4
work out the area of this shape
Answer:
the answer is 45 cm^2
how many questions are left lol
Que es un transportador?
Answer: it is a transporter or conveyer in english. Used for transporting goods
Step-by-step explanation:
The black graph is the graph of
y = f(x). Choose the equation for the
red graph.
a. y = f(x - 1)
b. y = f(²)
c.
d.
y - 1 = f(x)
²/₁ = f(x)
Answer:
c
Step-by-step explanation:
given f(x) then f(x) + c is a vertical translation of f(x)
• if c > 0 then a shift up of c units
• if c < 0 then a shift down of c units
here the red graph is i unit above the black graph , then c = + 1
and equation is
y = f(x) + 1 ( subtract 1 from both sides )
y - 1 = f(x)
MARKING BRAINLIEST! please help asap, and show your work
Answer:
Line AC is 8
Since the lines are parallel, the angles are the same, and the triangles are equally proportional. The ratio of 12 and 24 is 2, so you multiply 4 by 2 to get 8.
divide using polynomial long division
(x³ + x² + x + 2) : (x² − 1)
The required polynomial long division is shown, and the solution of the expression is given as x + 1 + [2x+ 3] / (x² − 1).
What is synthetic division?It is a method for performing the division of polynomials, with little writing and lesser calculations than complex division.
Here,
x² − 1) x³ + x² + x + 2 ( x + 1
x³ - x
----------------------
x² + x + x
x² + 1
------------------------------
2x + 1 + 3
Thus, the required polynomial long division is shown, and the solution of the expression is given as x + 1 + [2x+ 3] / (x² − 1).
Learn more about synthetic divisions here:
brainly.com/question/11850611
#SPJ1
I don't understand how to solve this. How do I find out the "Solution Region"
The graph of the solution region for the system of inequalities can be seen on the image at the end.
How to find the solution region?The solution region refers to the region where all the points are solutions of the system of inequalities.
The system of inequalities here is:
y < -x - 2
y < (1/4)x + 2
Notice that the two lines are already graphed, and "y" is smaller than the lines, so we need to shade all the region below the two lines.
The intersection of the shaded regions will be the region of solutions, the graph can be seen in the image below.
Learn more about systems of inequalities:
https://brainly.com/question/9774970
#SPJ1
m
A line passes through the point (-8, 7) and has a slope of
Write an equation in point-slope form for this line.
The equation of the line in point-slope form is obtained as y = (5/4)x - 20.
What is the point-slope form?
Point-slope is the general form of a linear equation which is y-y1=m(x-x1). It draws attention to the line's slope and one of the line's points (that is not the y-intercept).
The line passes through point (x1,y1) = (-8,-7)
The slope of the line is m = 5/4.
The formula for point-slope form of equation is -
y-y1=m(x-x1)
Substituting the values in the equation -
y - (-7) = 5/4[x - (-8)]
y + 7 = 5/4 (x + 8)
4(y + 7) = 5(x + 8)
4y + 28 = 5x + 8
4y - 5x = 8 - 28
4y - 5x = -20
4y = 5x -20
y = (5/4)x - 20
Therefore, the equation is obtained as y = (5/4)x - 20.
To learn more about point-slope form from the given link
https://brainly.com/question/6497976
#SPJ1
3. Vera's annual salary is $67,000. If this is 125% of her
starting salary at the company, what was her
starting salary?
A. $48,200
B. $49,800
C. $51,200
D. $53,600
4. Wh
Answer: Vera's starting salary at the company was $53600.
Step-by-step explanation:
We can start by using the following proportion:
(Current salary) / (Starting salary) = (Percent increase) / 100
So we can write:
67,000 / Starting salary = 125 / 100
To find the starting salary we can cross-multiply and divide:
67,000 = (125 * Starting salary) / 100
67,000 * 100 = 125 * Starting salary
67,000 * 100 = 125 * Starting salary
67,000,000 = 125 * Starting salary
Starting salary = 67,000,000 / 125
- C
At a zoo, youth ticket cot five dollar an adult ticket cot nine dollar a group purchaed ex youth ticket NY adult ticket pent $90 on ticket what i the domain of the relationhip?
The domain of this relationship would be all possible combinations of values for x and y that satisfy the equation 5x + 9y = 90.
To find the equation:
The domain of the relationship in this scenario is the number of youth and adult tickets that were purchased by the group.
It is given that the cost of a youth ticket is $5 and the cost of an adult ticket is $9. Therefore, the number of youth and adult tickets can be represented by the variables x and y respectively.
We also know that the group spent a total of $90 on tickets, so the equation representing the relationship between the number of youth and adult tickets purchased would be:
5x + 9y = 90
So the domain of this relationship would be all possible combinations of values for x and y that satisfy the equation 5x + 9y = 90.
It's important to note that the domain would be all non-negative integers of x and y as the number of youth and adult tickets cannot be negative numbers.
To learn more about the variables, visit:
brainly.com/question/29583350
#SPJ4
In the video game Digging Up Dinos, players gain and lose points while digging for dinosaur bones. In Level 1, Emmet earned 14 points for finding the foot bone of a dinosaur. Then, he lost 17 points for accidentally stepping on and breaking the bone.
What was Emmet's score at the end of Level 1?
Based on mathematical operations, Emmet's score at the end of Level 1 of the Digging Up Dinos video game was -3.
What are mathematical operations?The basic mathematical operations include addition, subtraction, division, and multiplication.
These mathematical operations manipulate variables, values, numbers, and constants, including mathematical operands and the equal symbol, to solve mathematical problems.
In this situation, the 17 points Emmet lost are subtracted from the 14 points that he gained to arrive at the final score at Level 1.
The number of points earned in Level 1 = 14
The number of points lost in Level 1 = 17
The net points at the end of Level 1 = -3 (14 - 17)
Thus, the subtraction operation shows that Emmet lost 3 more scores than he gained during Level 1.
Learn more about mathematical operations at https://brainly.com/question/4721701
#SPJ1
Evaluate.
[2−∣∣−14−2(−35)∣∣]÷(−6)
What is the value of the expression?
Enter your answer as a simplified fraction in the box.
GIVING 100
Answer:
The solution of the mathematical expressions will be 0.175.
Step-by-step explanation:
Given that;
The mathematical expressions are,
⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6
Now,
Solve the mathematical expression as;
⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6
Using the BODMAS rule to solve the expressions as;
⇒ [ 2 - | - 1/4 - 2 (-3/5) | ] ÷ -6
⇒ [ 2 - | - 1/4 + 6/5 | ÷ -6
⇒ [ 2 - 19/20 ] ÷ -6
⇒ [ 21/20] ÷ -6
⇒ 21/20 x 1/-6
⇒ - 7 / 40
Therefore,
The solution of the mathematical expressions will be 0.175.
But you didn't have to cut me off
Make out like it never happened and that we were nothing (aah-ooh)
And I don't even need your love (ooh)
But you treat me like a stranger, and that feels so rough (aah)
No, you didn't have to stoop so low (ooh)
Have your friends collect your records and then change your number (aah)
I guess that I don't need that, though
Now you're just somebody that I used to know
Answer:
[tex]-\dfrac{7}{40}[/tex]
Step-by-step explanation:
Given expression:
[tex]\left[2-\left|-\dfrac{1}{4}-2\left(-\dfrac{3}{5}\right)\right|\right] \div (-6)[/tex]
Carry out the operations inside the absolute value bars (following the order of operations):
[tex]\implies \left[2-\left|-\dfrac{1}{4}+\dfrac{6}{5}\right|\right] \div (-6)[/tex]
[tex]\implies \left[2-\left|\dfrac{19}{20}\right|\right] \div (-6)[/tex]
As the fraction inside the absolute value bars is already positive, we can simply remove the bars:
[tex]\implies \left[2-\dfrac{19}{20}\right] \div (-6)[/tex]
Rewrite 2 as 40/20 and carry out the subtraction inside the square brackets:
[tex]\implies \left[\dfrac{40}{20}-\dfrac{19}{20}\right] \div (-6)[/tex]
[tex]\implies \left[\dfrac{40-19}{20}\right] \div (-6)[/tex]
[tex]\implies \left[\dfrac{21}{20}\right] \div (-6)[/tex]
Rewrite -6 as a fraction:
[tex]\implies \dfrac{21}{20} \div -\dfrac{6}{1}[/tex]
When dividing fractions, multiply the first fraction by the reciprocal of the second fraction:
[tex]\implies \dfrac{21}{20} \times-\dfrac{1}{6}[/tex]
[tex]\implies \dfrac{21 \times (-1)}{20 \times 6}[/tex]
[tex]\implies -\dfrac{21}{120}[/tex]
Reduce the fraction to its simplest form by dividing the numerator and denominator by the highest common factor, 3:
[tex]\implies -\dfrac{21 \div 3}{120 \div 3}[/tex]
[tex]\implies -\dfrac{7}{40}[/tex]
On another day, Martin bought 123
5
pounds of grapes for a picnic. His friend bought 3
8
of that amount. Use compatible fractions to estimate how many pounds of grapes Martin’s friend bought.
123
5
→
3
8
→
Martin's friend bought about
pounds of grapes.
The amount of grape that the friend gets will be 4 29/40.
How to calculate the fraction?A fraction simply means a piece of a whole. In this situation, the number is represented as a quotient such that the numerator and denominator are split. In this situation, in a simple fraction, the numerator as well as the denominator are both integers.
In this situation, Martin bought 12 3/5 pounds of grapes for a picnic. His friend bought 3/8 of that amount.
The amount that the friend gets will be:
= 3/8 × 12 3/5
= 3/8 × 63/5
= 189 / 40
= 4 29 / 40
Learn more about fractions on
brainly.com/question/78672
#SPJ1
which of the following statements are true? (a) a quadrilateral is a parallelogram if it is a rhombus. (b) a quadrilateral is a rhombus if it is a parallelogram. (c) a quadrilateral is a parallelogram if and only if it is a rhombus. (d) a quadrilateral is a rhombus if and only if it is a parallelogram.
Among all the given statements for quadrilateral and parallelogram, none of the statements is true.
A rhombus is a quadrilateral with all sides of equal length, while a parallelogram is a quadrilateral with opposite sides parallel and equal in length.
(a) a quadrilateral is a parallelogram if it is a rhombus.
False, A rhombus is a quadrilateral with all sides of equal length and opposite sides parallel, so it is a parallelogram but not all parallelograms are rhombus.
(b) a quadrilateral is a rhombus if it is a parallelogram.
False, A parallelogram is a quadrilateral with opposite sides parallel and equal in length, so it may be a rhombus but not all parallelograms are rhombus.
(c) a quadrilateral is a parallelogram if and only if it is a rhombus.
False, A rhombus is a quadrilateral with all sides of equal length and opposite sides parallel, so it is a parallelogram but not all parallelograms are rhombus.
(d) a quadrilateral is a rhombus if and only if it is a parallelogram.
False, A parallelogram is a quadrilateral with opposite sides parallel and equal in length, so it may be a rhombus but not all parallelograms are rhombus.
Hence none of the above statements is true.
To learn more about the quadrilateral, visit:
brainly.com/question/29934440
#SPJ4
Find the area of parallelogram ABJF
Step-by-step explanation:
the area of a parallelogram is
base × height
the graphic shows us that the base (AB) is 3 units long.
and the height (BF) is also 3 units long.
so the area of ABJF is
3 × 3 = 9 units²
PLEASE HELP ASAP MATH SUBJECT
Answer:
√ 1. Quadratic
√ 2. Quadratic
√ 3. Quadratic
x 4. Not quadratic
x 5. Not quadratic
Step-by-step explanation:
A quadratic function is of the form
[tex]\large {ax^2 + bx + c}[/tex]
where a, b and c are real-valued constants and a ≠ 0
b and c can be 0
The degree of a quadratic function (the highest exponent ) will be 2
#4 has has degree 1
#5 has degree 3
So only 1, 2 and 3 are quadratic functions
In a 30-60-90 triangle, the smallest side measures inches 6v10 inches. Which is the exact measure for the largest side? a. 12v10 inches b. 2v30 inches c. 3v10 inches a. 6v5 inches
The exact measurements for the largest side is 12√10 inches. Hence option a is the correct option.
What is the right triangle?
A right triangle or right-angled triangle, or more formally an orthogonal triangle, formerly known as a rectangle triangle, is a triangle with one right angle, i.e. two perpendicular sides. Trigonometry is founded on the relationship between the sides and other angles of a right triangle.
Given that the angles of a triangle are 30-60-90.
The smallest angle is always opposite the shortest side, and vice versa. The longest side is also opposite the largest angle, and vice versa.
The opposite side of angle 30 is the shortest side of the triangle.
The opposite side of angle 90 is the longest side of the triangle.
Sine law:
a/sin A = b/ sin B =c/sin C
a is the opposite side of angle A, b is the opposite side of angle B, c is the opposite side of angle C.
Assume that the length of the longest side is a.
Applying sine law in the given triangle:
6√10/sin 30 = a/sin 90
6√10/(1/2)= a/1
a = 12√10
To learn more about sine law, click on the below link:
https://brainly.com/question/9339489
#SPJ4
The expession 3p +2f+s isnumber of points earned by a basketball team for p 3 point shots, f 2-point field goals and s 1-foul shots, your oppenent made 8 3-pointers,12 2-point field goals and 11 1-point foul shots you team made 10 3-pointers and 8 2-point field goals what is the mininum number of 1-point foul shots your team must make to win the game?
The minimum number of 1-point foul shots the home team must make to win the game, obtained using inequalities, is 14 shots.
What is an inequality?An inequality is a comparison between expressions that are non equal.
The function for the number of points earned is; 3·p + 2·f + s
Where;
p = 3 point shots
f = 2 point shots
s = 1 point foul shot
The number of 3-point shots by the opponent = 8
Number of 2-point field goals by the opponent = 12
Number of 1-point foul shot by the opponent = 11
The sum of the score of the opponent = 8 × 3 + 12 × 2 + 11 × 1 = 59
Number of 3-pointers by the home team = 10
Number of 2-pointers by the home team = 8
The number of 1-point foul shots, f, the home team must make to win the game can be found using the following inequality;
10 × 3 + 8 × 2 + f × 1 > 59
f > 59 - (10 × 3 + 8 × 2) = 13
f > 13The minimum number of 1-point foul shots the home team must make to win the game is therefore, more than 13 or at least 14
The minimum number of 1-point shots the home team requires to win the game are 14 shotsLearn more on inequalities here: https://brainly.com/question/27590365
#SPJ1
A regular octagon $ABCDEFGH$ has an area of one square unit. What is the area of the rectangle $ABEF$
The area of the rectangle ABEF = 2sa = 2ss/(2*tan(180/8)) = s^2/(tan(180/8)).
What is an octagon?
An octagon is a polygon with eight straight sides and eight angles. It is a closed two-dimensional shape with eight sides of equal length. A regular octagon is an octagon in which all sides and angles are equal.
When it comes to the area of a regular octagon, the area of a regular polygon can be calculated using the formula
A = (ns^2)/(4tan(180/n)) where A is the area, n is the number of sides and s is the length of each side.
In case of a regular octagon, the area of an octagon is (8s^2)/(4tan(180/8))
A rectangle ABEF is made up of two congruent sides with the length of the side of the octagon, and two congruent sides with the length of the apothem of the octagon.
An apothem of a regular polygon is the distance from the center of the polygon to the midpoint of any side. The apothem of a regular octagon can be calculated by using the formula
a = s/(2*tan(180/8)) where a is the apothem and s is the side of the octagon.
Hence, the area of the rectangle ABEF = 2sa = 2ss/(2*tan(180/8)) = s^2/(tan(180/8)).
To learn more about the octagon, visit:
https://brainly.com/question/27389561
#SPJ4
